How is the surface area of a three-dimensional object determined?

How is the surface area of a three-dimensional object determined?

• A. Subtracting interior areas
• B. Dividing by volume
• C. Multiplying area of one face by number of faces
• D. Adding the areas of all surfaces

Answer: (D)

Surface area is the total area that covers the outside of a three‑dimensional object. To get it, you add up the areas of every exterior surface. For a rectangular prism, the outside consists of six faces: two faces with area lw, two with area lh, and two with area wh. Adding them gives 2(lw + lh + wh). This idea extends to any shape: you sum the areas of all surface pieces, or, for curved objects, conceptually integrate over the surface to account for every tiny patch. Subtracting interior areas would cancel surfaces that are on the outside, dividing by volume mixes two different quantities, and multiplying one face’s area by the number of faces only works when all faces are the same size.

Surface area is the total area that covers the outside of a three‑dimensional object. To get it, you add up the areas of every exterior surface. For a rectangular prism, the outside consists of six faces: two faces with area lw, two with area lh, and two with area wh. Adding them gives 2(lw + lh + wh). This idea extends to any shape: you sum the areas of all surface pieces, or, for curved objects, conceptually integrate over the surface to account for every tiny patch. Subtracting interior areas would cancel surfaces that are on the outside, dividing by volume mixes two different quantities, and multiplying one face’s area by the number of faces only works when all faces are the same size.